To keep your TV rooted and/or rootable, it's absolutely necessary to NEVER do any official firmware upgrade. Even if you could think "bigger number is better", these updates never bring any new feature nor anything positive.

Furthermore, on E/F/H series you have to disable OTN support in service menu to prevent automatic online updates to be done without prior notice.

How To Disable Firmware Updates
In case you notice OTN support is greyed out, check second post of this thread for how to block updates on router level.To be mandatorily done on J/K/M if you expect root one day, don't tell you were not warned!!

E/F series

All ("smart"=having Smarthub) models on all firmwares are rootable, using procedure(s) found in public forum.

H-series(Access to project donor's only)

Rootable versions are corresponding to firmwares "up to October 2015". For now no root possible after that deadline.

T-MST14DEUC: firmware less than2790("less than" means NOT included !!)

T-GFPxDEUC: firmwares less than 1290

T-NT14UDEUC: firmware less than 1050

T-GFSDEUC: all firmwares (not concerned by Oct.15 limit)Beware that we don't have enough non-European models feedback to provide reliable info. Same goes for some low-ends such as T-NT14M.

If your current firmware is "out of range", check here and there for possible downgrade.